Select the correct combination of mathematical signs to sequentially replace the * signs and to balance the given equation. 62 * 11 * 42 * 6 * 18 * 21 * 7
=, ×, ÷, −, +, ÷
Balancing Equations with Mathematical Signs
The question asks us to find the correct combination of mathematical signs from the given options to replace the asterisks (*) in the equation sequentially so that the equation becomes balanced (true). The given equation structure is 62 * 11 * 42 * 6 * 18 * 21 * 7. There are six asterisks, which means we need a sequence of six mathematical signs.
We are given four options, each containing a sequence of six signs. We need to test each option by substituting the signs into the equation from left to right and checking if the left side of the equation equals the right side.
Testing the Mathematical Sign Combinations
Let's test each option one by one using the order of operations (BODMAS/PEMDAS: Brackets, Orders/Exponents, Division and Multiplication, Addition and Subtraction) where multiplication and division have equal priority and are performed from left to right, and addition and subtraction have equal priority and are performed from left to right.
Testing Option 1: +, −, =, ×, −, ÷
Substituting these signs into the equation 62 * 11 * 42 * 6 * 18 * 21 * 7 gives:
62 + 11 - 42 = 6 × 18 - 21 ÷ 7
Let's evaluate the Left Hand Side (LHS):
LHS = 62 + 11 - 42
LHS = 73 - 42
LHS = 31
Now, let's evaluate the Right Hand Side (RHS):
RHS = 6 × 18 - 21 ÷ 7
Perform multiplication and division first:
6 × 18 = 108
21 ÷ 7 = 3
Substitute back:
RHS = 108 - 3
RHS = 105
Comparing LHS and RHS:
31 ≠ 105
So, Option 1 does not balance the equation.
Testing Option 2: =, ×, ÷, −, +, ÷
Substituting these signs into the equation 62 * 11 * 42 * 6 * 18 * 21 * 7 gives:
62 = 11 × 42 ÷ 6 - 18 + 21 ÷ 7
Let's evaluate the Left Hand Side (LHS):
LHS = 62
Now, let's evaluate the Right Hand Side (RHS):
RHS = 11 × 42 ÷ 6 - 18 + 21 ÷ 7
Perform multiplication and division first (from left to right):
11 × 42 = 462462 ÷ 6 = 7721 ÷ 7 = 3
Substitute these results back into the RHS expression:
RHS = 77 - 18 + 3
Perform addition and subtraction next (from left to right):
77 - 18 = 5959 + 3 = 62
RHS = 62
Comparing LHS and RHS:
62 = 62
The equation is balanced. So, Option 2 is the correct combination of signs.
Since we found the correct option, we can stop here. However, for completeness and understanding, let's briefly look at the other options as well to confirm they do not balance the equation.
Testing Option 3: −, +, =, ×, −, +
Equation: 62 - 11 + 42 = 6 × 18 - 21 + 7
LHS = 62 - 11 + 42 = 51 + 42 = 93
RHS = 6 × 18 - 21 + 7 = 108 - 21 + 7 = 87 + 7 = 94
93 ≠ 94. Option 3 is incorrect.
Testing Option 4: +, −, ÷, =, ×, +
Equation: 62 + 11 - 42 ÷ 6 = 18 × 21 + 7
LHS = 62 + 11 - 42 ÷ 6 = 62 + 11 - 7 = 73 - 7 = 66
RHS = 18 × 21 + 7 = 378 + 7 = 385
66 ≠ 385. Option 4 is incorrect.
Based on our tests, only Option 2 balances the given equation.
| Option | Signs Used | Equation | LHS Calculation | RHS Calculation | Balanced? |
|---|---|---|---|---|---|
| 1 | +, −, =, ×, −, ÷ | \(62 + 11 - 42 = 6 \times 18 - 21 \div 7\) | \(73 - 42 = 31\) | \(108 - 3 = 105\) | No |
| 2 | =, ×, ÷, −, +, ÷ | \(62 = 11 \times 42 \div 6 - 18 + 21 \div 7\) | \(62\) | \(77 - 18 + 3 = 59 + 3 = 62\) | Yes |
| 3 | −, +, =, ×, −, + | \(62 - 11 + 42 = 6 \times 18 - 21 + 7\) | \(51 + 42 = 93\) | \(108 - 21 + 7 = 87 + 7 = 94\) | No |
| 4 | +, −, ÷, =, ×, + | \(62 + 11 - 42 \div 6 = 18 \times 21 + 7\) | \(62 + 11 - 7 = 73 - 7 = 66\) | \(378 + 7 = 385\) | No |
Revision Table: Key Concepts in Balancing Equations
| Concept | Description | Importance |
|---|---|---|
| Order of Operations | Rules (like BODMAS/PEMDAS) dictating the sequence of mathematical operations (Brackets, Orders, Division/Multiplication, Addition/Subtraction). | Ensures calculations are performed consistently, leading to the correct result. |
| Equation | A mathematical statement that shows that two expressions are equal. | The goal is to find signs that make the left side equal to the right side. |
| Balancing an Equation | Finding the values or operations that make the equality true. | Confirms the correctness of the chosen combination of signs. |
| Substitution | Replacing variables or symbols with specific values or operations. | Used here to replace the '*' with the given mathematical signs from options. |
Additional Information: Mathematical Puzzles and BODMAS
Mathematical puzzles like this one, involving inserting signs to balance an equation, are common tests of arithmetic skills and understanding the order of operations. The ability to correctly apply the BODMAS or PEMDAS rule is crucial for solving these puzzles accurately.
BODMAS stands for:
- Brackets
- Orders (powers, square roots, etc.)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Following this order ensures that expressions are evaluated consistently. For example, in the expression 10 + 2 × 5, without BODMAS, one might do the addition first (10 + 2 = 12) and then multiply by 5 (12 × 5 = 60), which is incorrect. With BODMAS, you perform multiplication first (2 × 5 = 10) and then addition (10 + 10 = 20), which is the correct result.
In this problem, applying the order of operations correctly was essential when evaluating the expressions on both sides of the equation for each option.
Similar Questions
In a certain code language, ‘+' represents '×', '-’represents ‘+', '×’ represents '÷’ and '÷’ represents '-'. What is the answer to the following question?
75 - 5 + 25 ÷ 125 = ?If 6 @ 4 @ 7 = 101 and 2 @ 5 @ 11 = 150, then what is the value of A in A @ 8 @ 9 = 289?
If 12 (20) 16 and 21 (35) 28, then what is value of A in 48 (80) A ?
The two given expressions on both the side of the ‘=’ sign will have the same value if two numbers from either side or both side are interchanged. Select the correct numbers to be interchanged from the given options.
4 + 6 × 7 – 27 ÷ 3 = 7 × 8 – 4 + 39 ÷ 3If 11\(25 = 18, 12\)20 = 16 then what is the value of 4$50 = ?
If (2)# * 4 = 2 and (4)# * 4 = 16, then what is the value of A in (6)# * A = 18?
If "α" denotes "subtracted from", "β" denotes "multiplied by", "θ" denotes "added to" and "δ" denotes "divided by", then 10 θ 8 β 4 δ 8 α 9 = ?
In the following question, correct the equation by interchanging two signs.
4 × 3 - 6 ÷ 2 + 7 = 8Which two signs and two numbers should be interchanged to make the given equation correct?
17 + 11 – 12 × 36 ÷ 6 = 80
Which two signs should be interchanged to make the following equation correct?
18 + 24 – 6 × 6 ÷ 3 = 39
Important Questions from Logical Puzzle
Seven persons P, Q, R, S, T, U and V like different watches namely W1, W2, W3, W4, W5, W6 and W7 (not necessarily in the same order). P and R do not like odd numbered watch. T likes W5. U does not like W2 or W3 or W6 or W7. P likes prime numbered watch. Q likes W4. S likes W2 or W7. Which of the following statement(s) is/are correct ?
I. S likes W7.
II. R likes W2.
III. U likes W1.
IV. V likes W3.
If ‘+’ means ‘×’, ‘×’ means ‘÷’, ‘÷’ means ‘–’ and ‘–’ means ‘+’, then
16 + 18 × 3 ÷ 6 = ?
In a certain code language, ‘Today is last match’ is written as ‘Sa Te Mo Pt’, ‘Last king like your team’ is written as ‘De Ra Mo Lo Zs’, ‘Our team won today match’ is written as ‘Te Ra Pt Ae We’. What is the code for ‘Our won is Last’ in that code language?
In a certain code language, ‘LETTER’ is written as ‘ZLZYIO’. What is the code for ‘ACTION’ in that code language?
If A denotes ‘+’, B denotes ‘×’, C denotes ‘-’, and D denotes ‘÷’, then what will come in place of ‘?’ in the following equation?
34 A 15 B 3 C 11 B 2 A (51 D 17) = ?
